Rellich and Calderón–Zygmund inequalities for an operator with discontinuous coefficients

We prove necessary and sufficient conditions for the validity of Rellich and Calderón–Zygmund inequalities in L p for the operator L = Δ + ( a - 1 ) ∑ i , j = 1 N x i x j | x | 2 D i j + c x | x | 2 · ∇ - b | x | 2 , where a > 0 , b , c ∈ R .

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Bibliographic Details
Published in:Annali di matematica pura ed applicata 2016-08, Vol.195 (4), p.1305-1331
Main Authors: Metafune, G., Sobajima, M., Spina, C.
Format: Article
Language:English
Subjects:
Inequalities
Mathematics
Mathematics and Statistics
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Summary:We prove necessary and sufficient conditions for the validity of Rellich and Calderón–Zygmund inequalities in L p for the operator L = Δ + ( a - 1 ) ∑ i , j = 1 N x i x j | x | 2 D i j + c x | x | 2 · ∇ - b | x | 2 , where a > 0 , b , c ∈ R .
ISSN:0373-3114
1618-1891
DOI:10.1007/s10231-015-0517-8